One can see from Table REF  that our results are almost
two order larger in magnitude than those from Ref. [1]}.
Unfortunately, the authors of [1]} did not give
the numerical coefficients for the Wilson coefficients \(C_1\)  and \(C_2\) ,
there are only the combinations of \(\alpha _1=C_1+\xi C_2\)  and
\(\alpha _2=C_2+\xi C_1\)  with \(\xi =1/N_c\) . However, they refer to the
papers by Buras et al. [3]}, [4]} in which
the notation are accepted as \(C_2=1\)  and
\(C_1=0\)  if QCD is neglected.
We are using the Wilson coefficients
from Ref. [5]} (see, Table 3, and references therein)
where their values have been calculated by using the various corrections
and found that \(C_1 = -0.2632\)  and \( C_2 = 1.0111\) .
If one uses these values for \(\alpha _1\)  and \(\alpha _2\)  of
Ref. [1]} then one arrives at
\(\alpha _1\approx 0.074\)  for \(N_c=3\) , i.e. strongly
suppressed, whereas the value of \(\alpha _2=0.923\)  is of the leading order.
If compare the analytical expressions for the decay amplitudes from
[1]} (see, Eqs. (13)-(24)) with our results given by
Eq. REF  and Table REF ,
then one finds that in Ref. [1]}
the amplitudes with the charged emitted mesons are proportinal to
\(\alpha _1\)  which is suppressed whereas in our approach those amplitudes
are proportinal to \(a_2\)  which is of leading order.
It could explain two order difference for branching fractions obtained
in these two approaches.
